Lee, That link looks like it's working for me now. Must have been a temporary server error.
Will <http://www.verizonmedia.com> Will Lauer Senior Principal Architect, Audience & Advertising Reporting Data Platforms & Systems Engineering M 508 561 6427 1908 S. First St Champaign, IL 61822 <http://www.facebook.com/verizonmedia> <http://twitter.com/verizonmedia> <https://www.linkedin.com/company/verizon-media/> <http://www.instagram.com/verizonmedia> On Thu, Nov 19, 2020 at 9:57 AM leerho <lee...@gmail.com> wrote: > Hi Justin, the site you referenced returns an error 500 (internal server > error). It might be down, or out-of-service. You might also check to make > sure it is the correct URL. > > Thanks! > Lee. > > On Thu, Nov 19, 2020 at 6:05 AM Justin Thaler <justin.r.tha...@gmail.com> > wrote: > >> I think the way to think about this is the following. If you downsample >> and then sketch, there are two sources of error: sampling error and >> sketching error. The former refers to how much the answer to your query >> over the sample deviates from the answer over the original data, while the >> second refers to how much the estimate returned by the sketch deviates from >> the exact answer on the sample. >> >> If the sampling error is very large, then no matter how accurate your >> sketch is, your total error will be large, so you won't be gaining anything >> by throwing resources into minimizing sketching error. >> >> If sampling error is very small, then there's not really a need to drive >> sketching error any lower than you would otherwise choose it to be. >> >> So as a practical matter, my personal recommendation would be to make >> sure your sample is big enough that the sampling error is very small, and >> then set the sketching error as you normally would ignoring the subsampling. >> >> In case it's helpful, I should mention that there's been (at least) one >> academic paper devoted to precisely the question of what is the best >> approach to sketching for various query classes if data must first be >> subsampled if you'd like to check it out: >> https://core.ac.uk/download/pdf/212809966.pdf >> <https://urldefense.proofpoint.com/v2/url?u=https-3A__core.ac.uk_download_pdf_212809966.pdf&d=DwMFaQ&c=sWW_bEwW_mLyN3Kx2v57Q8e-CRbmiT9yOhqES_g_wVY&r=vGHo2vqhE2ZeS_hHdb4Y3eoJ4WjVKhEg5Xld1w9ptEQ&m=TS-clarTE9n5rihY9KO9VJBABYz9__eAAcLmXJGPrLA&s=yWiRfonSO6QIO9joZFuuz_gglz6SQnYjxysLQZza5IM&e=> >> >> I should reiterate that there are certain types of queries that >> inherently don't play well with random sampling (i.e., it's basically >> impossible to give a meaningful bound on the sampling error, at least >> without making assumptions about the data, which is something that error >> guarantees provided by the library assiduously avoids). >> >> On Thu, Nov 19, 2020 at 7:20 AM Sergio Castro <sergio...@gmail.com> >> wrote: >> >>> Thanks a lot for your answers to my first question, Lee and Justin. >>> >>> Justin, regarding this observation: "*All of that said, the library >>> will not be able to say anything about what errors the user should expect >>> if the data is pre-sampled, because in such a situation there are many >>> factors that are out of the library's control.* " >>> Trying to alleviate this problem. I know I can tune the DataSketches >>> computation by means of trading-off memory vs accuracy. >>> So is it correct that in the scenario where I am constrained to >>> pre-sample the data, I should aim for the best optimization for accuracy >>> even if this will require more memory, with the objective of alleviating >>> the impact of my double sampling problem (meaning the pre-sampling I am >>> constrained to do before + the sampling performed by Datasketches itself)? >>> While in the scenarios where I am not constrained to use pre-sampling I >>> still could use the default DataSketches configuration with a more balanced >>> trade-off between accuracy and memory requirements? >>> >>> Would you say this is a good best-effort strategy? Or in both cases you >>> would recommend me to use the same configuration ? >>> >>> Thanks for your time and feedback, >>> >>> Sergio >>> >>> >>> On Thu, Nov 19, 2020 at 1:24 AM Justin Thaler <justin.r.tha...@gmail.com> >>> wrote: >>> >>>> Lee's response is correct, but I'll elaborate slightly (hopefully this >>>> is helpful instead of confusing). >>>> >>>> There are some queries for which the following is true: if the data >>>> sample is uniform from the original (unsampled) data, then accurate answers >>>> with respect to the sample are also accurate with respect to the original >>>> (unsampled) data. >>>> >>>> As one example, consider quantile queries: >>>> >>>> If you have n original data points from an ordered domain and you >>>> sample at least t ~= log(n)/epsilon^2 of the data points at random, it is >>>> known that, with high probability over the sample, for each domain item i, >>>> the fractional rank of i in the sample (i.e., the number of sampled points >>>> less than or equal to i, divided by the sample size t) will match the >>>> fractional rank of i in the original unsampled data (i.e., the number of >>>> data points less than or equal to i, divided by n) up to additive error at >>>> most epsilon. >>>> >>>> In fact, at a conceptual level, the KLL quantiles algorithm that's >>>> implemented in the library is implicitly performing a type of downsampling >>>> internally and then summarizing the sample (this is a little bit of a >>>> simplification). >>>> >>>> Something similar is true for frequent items. However, it is not true >>>> for "non-additive" queries such as unique counts. >>>> >>>> All of that said, the library will not be able to say anything about >>>> what errors the user should expect if the data is pre-sampled, because in >>>> such a situation there are many factors that are out of the library's >>>> control. >>>> >>>> On Wed, Nov 18, 2020 at 3:08 PM leerho <lee...@gmail.com> wrote: >>>> >>>>> Sorry, if you presample your data all bets are off in terms of >>>>> accuracy. >>>>> >>>>> On Wed, Nov 18, 2020 at 10:55 AM Sergio Castro <sergio...@gmail.com> >>>>> wrote: >>>>> >>>>>> Hi, I am new to DataSketches. >>>>>> >>>>>> I know Datasketches provides an *approximate* calculation of >>>>>> statistics with *mathematically proven error bounds*. >>>>>> >>>>>> My question is: >>>>>> Say that I am constrained to take a sampling of the original data set >>>>>> before handling it to Datasketches (for example, I cannot take more than >>>>>> 10.000 random rows from a table). >>>>>> What would be the consequence of this previous sampling in the >>>>>> "mathematically proven error bounds" of the Datasketches statistics, >>>>>> relative to the original data set? >>>>>> >>>>>> Best, >>>>>> >>>>>> Sergio >>>>>> >>>>>
